Let's assume that there is a conspiracy against him. He still got into a verbal altercation with an opposing player, that alone is enough to ban him for life. The Jazz and Vivint arena are just like any other business, they can refuse service for any reason. The Jazz and Westbrook aren't responsible for other people threatening him on Twitter.
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People post fake tweets all the time. So I can't say one way or the other. And it has been confirmed there was more than one fake account pretending to be this guy and saying horrible things.
However, Gail Miller banned the fan then made a statement about racist, homophobic or other statements from being made. Clearly it was regarding this fan. If they did have knowledge he didn't say anything racist, but frame the ban in a way that it was racist comment based, he may have a claim.
Yes, the Jazz could ban you, but as a private figure, they can't recklessly defame you, and that has been a winning argument in many defamation cases.
If they had video or other corroborating witnesses saying he told Westbrook to ice his knees (which Westbrook was doing), but banned him anyway, when historically they have let fans say any similar and much worse banter to a player (heard much worse near courtside and the court monitors don't do anything) then release a statement on racist comments right after, what does the world infer?
Most likely, the Jazz legal team required the organization to due an ample investigation and the lawsuit is a farce, but if that is not the case, the Jazz should refuse to settle. Let the truth be known in court, get witnesses, and if allowed, forensic data to prove whether the purported Tweets were his or not, and let the guy be ruined forever.